Abstract
We show the existence result of viable solutions to the differential inclusion
(x) over dot (t) is an element of G(x(t)) + F(t, x(t)) x(t) is an element of S on [0, T],
where F : [0, T] x H -> H (T > 0) is a continuous set-valued mapping, G : H -> H is a Hausdorff upper semi-continuous set-valued mapping such that G(x) subset of partial derivative g(x), where g : H -> R is a regular and locally Lipschitz function and S is a ball, compact subset in a separable Hilbert space H.